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Simplifying 8w3 + 2w2 + -1w = 0 Reorder the terms: -1w + 2w2 + 8w3 = 0 Solving -1w + 2w2 + 8w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), 'w'. w(-1 + 2w + 8w2) = 0 Factor a trinomial. w((-1 + -2w)(1 + -4w)) = 0Subproblem 1
Set the factor 'w' equal to zero and attempt to solve: Simplifying w = 0 Solving w = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w = 0Subproblem 2
Set the factor '(-1 + -2w)' equal to zero and attempt to solve: Simplifying -1 + -2w = 0 Solving -1 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2w = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2w = 0 + 1 -2w = 0 + 1 Combine like terms: 0 + 1 = 1 -2w = 1 Divide each side by '-2'. w = -0.5 Simplifying w = -0.5Subproblem 3
Set the factor '(1 + -4w)' equal to zero and attempt to solve: Simplifying 1 + -4w = 0 Solving 1 + -4w = 0 Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -4w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4w = 0 + -1 -4w = 0 + -1 Combine like terms: 0 + -1 = -1 -4w = -1 Divide each side by '-4'. w = 0.25 Simplifying w = 0.25Solution
w = {0, -0.5, 0.25}
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